higgs - page 27

standard-model Higgs boson are M H. 114 GeV/ c 2 via direct
searches208 and M H , 193 GeV/c 2 from fits to precise elec-
troweak data.209
Discovering the nature of the Higgs boson is a key to
further progress in understanding what may lie beyond the
standard model. There may exist one Higgs boson or more
than one. There may exist other particles in the spectrum
related to it. The Higgs boson may be elementary or com-
posite. If composite, it points to a new level of substructure
of the elementary particles.
I. Precision electroweak measurements
Precision electroweak measurements can yield informa-
tion on many new-physics possibilities in addition to the
Higgs boson. The seminal paper of Veltman210 showed how
the ratio of W and Z masses could shed light on the top
quark’s mass. A systematic study of electroweak radiative
corrections within the standard model was performed by
Marciano and Sirlin211 and used to analyze a wide variety of
electroweak data, initially in Ref. 212 and most recently in
Ref. 209. Widely-used parametrizations of deviations from
Standard-Model predictions213–215 have been used to con-
strain new particles in higher-order loop diagrams associated
with W, Z, and photon self-energies. Some reviews include
Refs. 216–219.
206. ‘‘Report of the Tevatron Higgs Working Group,’’ M. Carena et al.,
Fermilab report FERMILAB-CONF-00-279-T, hep-ph/0010338 ~un-
published!. ~A!
207. ‘‘The Higgs Working Group: Summary Report,’’ D. Cavalli et al., in
Proceedings of Workshop on Physics at TeV Colliders, Les Houches,
France, 21 May–1 June 2001, edited by P. Aurenche et al. ~Paris,
IN2P3, 2001!, pp. 1–120. ~A!
208. LEP Higgs Working Group, results quoted in web page of LEP Elec-
troweak Working Group, http://lepewwg.web.cern.ch/
LEPEWWG/. ~I!
209. LEP Electroweak Working Group, http://
lepewwg.web.cern.ch/LEPEWWG/. ~I!
210. ‘‘Limit on Mass Differences in the Weinberg Model,’’ M. Veltman,
Nucl. Phys. B123, 89 ~1977!. ~A!
211. ‘‘Radiative Corrections to Neutrino Induced Neutral Current Phenom-
ena in the SU~2!L3 U~1! Theory,’’ W. J. Marciano and A. Sirlin, Phys.
Rev. D 22, 2695 ~1980!; 31, 213 ~1985!. ~A!
212. ‘‘A Comprehensive Analysis of Data Pertaining to the Weak Neutral
Current and the Intermediate Vector Boson Masses,’’ U. Amaldi
et al., Phys. Rev. D 36, 1385 ~1987!. ~I!
213. ‘‘A New Constraint on a Strongly Interacting Higgs Sector,’’ M. E.
Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964–967 ~1990!. ~A!
214. ‘‘Estimation of Oblique Electroweak Corrections,’’ M. E. Peskin and
T. Takeuchi, Phys. Rev. D 46, 381–409 ~1992!. ~A!
215. ‘‘Vacuum Polarization Effects of New Physics on Electroweak Pro-
cesses,’’ G. Altarelli and R. Barbieri, Phys. Lett. B 253, 161–167
~1991!. ~A!
216. ‘‘Electroweak Theory. Framework of On-Shell Renormalization and
Study of Higher-Order Effects,’’ K. I. Aoki et al., Prog. Theor. Phys.
Suppl. 73, 1–225 ~1982!. ~A!
217. ‘‘Electroweak Radiative Corrections, M Z , MW , and the Heavy Top,’’
W. Hollik, Adv. Ser. Direct. High Energy Phys. 10, 1–57 ~1992!. ~A!
218. The Standard Model in the Making: Precision Study of the Elec-
troweak Interactions, D. Yu. Bardin and G. Passarino ~Clarendon
Press, Oxford, 1999!. ~A!
219. ‘‘Radiative Corrections in Gauge Theories,’’ H. Anlauf, lectures at
Adriatic School on Particle Physics and Physics Informatics, Septem-
ber 11–21, 2001, http://heplix.ikp.physik.tu-
darmstadt.de/;anlauf/ha-lectures.html . ~A!
X. PROPOSED EXTENSIONS
A. Supersymmetry
Unification of the electroweak and strong interactions at a
high mass scale leads to the hierarchy problem, in which this
scale contributes through loop diagrams to the Higgs boson
mass and requires it to be fine-tuned at each order of pertur-
bation theory. A similar problem is present whenever there is
a large gap between the electroweak scale and any higher
mass scale contributing to the Higgs boson mass. Supersym-
metry solves this problem by introducing for each particle of
spin J a superpartner of spin J 6 1/2 whose contribution to
such loop diagrams cancels the original one in the limit of
degenerate masses. Recent reviews of supersymmetry and its
likely experimental signatures include Refs. 40, 62–67,
while earlier discussions are given by Refs. 68, 69, and 70.
For an article at the popular level see Ref. 119.
B. Dynamical electroweak symmetry breaking
If the Higgs boson is not fundamental but arises as the
result of a new super-strong force which, in analogy with
color, causes the dynamical generation of one or more scalar
particles, the hierarchy problem can be avoided. This
scheme, sometimes called ‘‘technicolor,’’ was proposed in
the 1970s.220–222 For recent reviews, see. e.g., Refs. 223–
225.
220. ‘‘Implications of Dynamical Symmetry Breaking,’’ S. Weinberg,
Phys. Rev. D 13, 974–996 ~1976!. ~A!
221. ‘‘Implications of Dynamical Symmetry Breaking: An Addendum,’’ S.
Weinberg, Phys. Rev. D 19, 1277–1280 ~1979!. ~A!
222. ‘‘Dynamics of Spontaneous Symmetry Breaking in the Weinberg–
Salam Theory,’’ L. Susskind, Phys. Rev. D 20, 2619–2625 ~1979!.
~A!
223. ‘‘Lectures on Technicolor and Compositeness,’’ R. S. Chivukula, in
Ref. 47, pp. 731–772. ~A!
224. ‘‘Two Lectures on Technicolor,’’ K. Lane, Fermilab report
FERMILAB-PUB-02- 040-T, preprint hep-ph/0202255 ~unpub-
lished!. ~A!
225. ‘‘Strong dynamics and electroweak symmetry breaking,’’ C. T. Hill
and E. H. Simmons, Fermilab report FERMILAB-PUB-02-045-T,
preprint hep-ph/0203079, submitted to Phys. Rep. ~A!
C. Fermion mass and mixing patterns
The transitions between the ( u, c , t ) and (d , s , b ) quarks
owing to virtual W emission or absorption are described by
the Cabibbo–Kobayashi–Maskawa ~ CKM! matrix men-
tioned in Sec. IXA. ~ For one parametrization of this matrix
see Ref. 226.! The CKM matrix arises because the matrices
that diagonalize the mass matrices of (u , c , t ) and of (d , s, b)
are not the same. A theory of quark masses would thus entail
a specific form of the CKM matrix. For the corresponding
matrix for leptons, see Refs. 227–229. While a theory of
quark and lepton masses still eludes us, attempts have been
made to guess some of its general features.230–235
226. ‘‘Parametrization of the Kobayashi-Maskawa Matrix,’’ L. Wolfen-
stein, Phys. Rev. Lett. 51, 1945–1947 ~1983!. ~I!
227. ‘‘Remarks on the Unified Model of Elementary Particles,’’ Z. Maki,
M. Nakagawa, and S. Sakata, Prog. Theor. Phys. 28, 870–880
~1962!. ~A!
228. ‘‘Muon and Electron Number Nonconservation in a V – A Gauge
Model,’’ B. W. Lee, S. Pakvasa, R. Shrock, and H. Sugawara, Phys.
Rev. Lett. 38, 937–939 ~1977!. ~A!
312 312 Am. J. Phys., Vol. 71, No. 4, April 2003 Jonathan L. Rosner